Cone-and-plate method

To measure elastic and viscous properties which are characteristic of the material under consideration and independent of the nature of the apparatus employed, the applied stress and the resulting deformation must be uniform throughout the sample. Concentric cylinder and cone and plate methods approximate these requirements. For materials which are self-supporting, measurements on, for example, the shearing of rectangular samples are ideal. 

The apparent viscosity is determined from Eq. 4. The value of shear rate that corresponds to this viscosity is obtained from the known viscosity vs shear rate rheogram for the non-Newtonian fluids generated using the cone-and-plate method. The value of k is determined from Eq. 5. 

CEN EN 13702. 2010. Bitumen and bituminous binders - Determination of dynamic viscosity of modified bitumen by cone and plate method. Brussels CEN. 

To calculate the first normal stress difference for low shear rates, using the cone-and-plate method [2], use... 

Low shear viscosity was measured with a "Haake VT 500 viscometer using a cylindrically shaped E30 spindle at a rotation speed of 179 rpm and at 23 °C. High shear viscosity was measured in accordance with the ICl cone and plate method (ASTM D 4287) at a shear rate of 20.000 s ... 

Viscoelastic Measurement. A number of methods measure the various quantities that describe viscoelastic behavior. Some requite expensive commercial rheometers, others depend on custom-made research instmments, and a few requite only simple devices. Even quaHtative observations can be useful in the case of polymer melts, paints, and resins, where elasticity may indicate an inferior batch or unusable formulation. Eor example, the extmsion sweU of a material from a syringe can be observed with a microscope. The Weissenberg effect is seen in the separation of a cone and plate during viscosity measurements or the climbing of a resin up the stirrer shaft during polymerization or mixing. 

Assuming that the melt viscosity is a power law function of the rate of shear, calculate the percentage difference in the shear stresses given by the two methods of measurement at the rate of shear obtained in the cone and plate experiment. 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

Figure 3.27 Cone and plate and capillary rheology data for a specialty PE resin. A slight shift in the rheology occurs between the two methods at a shear rate of 100 1 /s...

Various methods are used to examine the viscosity characteristics of metallized gels. Two types that have received extensive application are the cone and plate viscometer and the capillary viscometer. Both instruments can measure rheological characteristics at high shear rates, and the former is useful for low shear rate measurements as well. 

It must be concluded that Bueche s concept does not suffice to explain the melt flow behaviour of very high molecular weight samples. To the knowledge of the present author, Mieras and Van Rijn (735) have first pointed to this fact. The results given in Fig. 4.4 are in fair agreement with those obtained by the mentioned authors on the same samples, using the Weissenberg method (cone-and-plate apparatus, see Section 2.4). 

As already mentioned in Chapter 1, there are mainly three geometries suitable for the measurement of flow birefringence, viz. those of the concentric cylinder apparatus, the adapted cone-and-plate apparatus and the slit-capillary with a rectangular cross-section. The general principles of the pertinent techniques have been described in the same chapter. The purpose of the present chapter is to give details of the design and construction in order to enable the reader to form a judgement as to the efficiency of the proposed methods, i.e. the relation between information and experimental effort. 

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

The prime control is the viscosity of the material. This is best carried out using a temperature-controlled cone and plate viscometer. The sample volume needs to be small to allow quick stabilization of the material to a temperature of 23°C. A secondary test to determine the NCO content using a titration method based on that given in Appendix 6 must be carried out as rapidly as possible. 

Measurement of the flow properties of non-Newtonian fluids is typically accomplished via rotational techniques. The rotational methods fall into two basic types, concentric cylinder and cone and plate rheometers. In a concentric cylinder rheometer, a bob is placed inside a cylinder so that the fluid to be studied may be placed into the gap between the cylinders. This arrangement helps approximate a uniform shear rate throughout a sample by shearing only a thin film of sample fluid between... 

In the cone and plate rheometer, a cone-shaped bob is placed against a flat plate so that the fluid to be studied may be placed into the gap between the lower face of the cone and the upper face of the plate. Again, in the Searle method, the cone is rotated while in the Couette method the plate turns. In each case, the torque on the cone is measured. Figure 6.5 shows a Searle-type cone and plate arrangement. For this arrangement the shear stress is given by ... 

In systems with suspended solids, rheologic measurements are difficult to perform owing to settling in the measurement devices. Conventional methods for measuring rheologic properties (cone-and-plate, concentric cylinder, and rotating-bob viscometers) do not produce accurate and reliable data for some solid suspensions. 

Newtonian and non-Newtonian calibration fluids were used to determine the necessary calibration constants for the impeller method. It has been previously determined that the impeller method is only valid for a Reynolds number (Re) <10. Impeller rotational speed and torque data from Newtonian calibration fluids of known viscosity were employed to determine the Newtonian calibration constant, c. Cone-and plate-viscometer data from non-Newtonian calibration fluids were used to determine a viscosity vs shear rate relationship. Impeller rotational speed and torque data of the non-Newtonian calibration fluids combined with a determined viscosity vs shear rate correlation were utilized to calculate the shear rate constant, k. The impeller method calibration constants allow the calculation of viscosity, shear rate, and shear stress data of non-Newtonian suspensions. Metz et al. (2) have thoroughly discussed the equations utilized in the impeller method. 

This section describes two common experimental methods for evaluating i], Fj, and IG as functions of shear rate. The experiments involved are the steady capillary and the cone-and-plate viscometric flows. As noted in the previous section, in the former, only the steady shear viscosity function can be determined for shear rates greater than unity, while in the latter, all three viscometric functions can be determined, but only at very low shear rates. Capillary shear viscosity measurements are much better developed and understood, and certainly much more widely used for the analysis of polymer processing flows, than normal stress difference measurements. It must be emphasized that the results obtained by both viscometric experiments are independent of any constitutive equation. In fact, one reason to conduct viscometric experiments is to test the validity of any given constitutive equation, and clearly the same constitutive equation parameters have to fit the experimental results obtained with all viscometric flows. 

With rubbers a similar situation is met, but now with the aid of a rotation viscometer. The Mooney viscosity is measured as the torque needed to rotate two parallel plates, between which the rubber mass is present, with respect to each other. This provides a rough indication of the viscosity, and thus of the molar mass. This measurement can also be used to characterize the vulcanization behaviour under vulcanization conditions the increase of the Mooney viscosity indicates the onset of network formation. When the network develops further, a continuous rotation can, of course, no longer be applied because the viscosity increases unlimitedly therefore an oscillation method is mostly used with a cone-and-plate geometry. Initially, the viscosity is being measured, and later on the build-up of the E-modulus of the network. Another characterization of the viscosity of unvulcanized rubbers is the Hoekstra method. The rubber is present between two parallel plates, which are moved towards each other with a certain speed the force needed to do so is an indication of the viscosity. 

The rotational viscosity method described above to measure working life or pot life is a form of rheological measurement of cure. However, cone and plate rheometry is preferred for accurate measurements because the specimen size and geometry are similar to those that occur in an adhesive joint. 

Though the parallel plate method is described here, cone and plate options are also available. These will more accurately describe the shear stress dependence of the material if that is the experimental goal. 

One very important point that must be considered in any rheological measurement is the possibility of slip during the measurements. This is particularly the case with highly concentrated dispersions, whereby the flocculated system may form a plug in the gap of the platens, leaving a thin liquid film at the walls of the concentric cylinder or cone-and-plate geometry. This behaviour is caused by some syneresis of the formulation in the gap of the concentric cylinder or cone and plate. In order to reduce sHp, roughened walls should be used for the platens an alternative method would be to use a vane rheometer. 

An instrument employed in the test method is either a cone-and-plate rheometer or a parallel-plate rheometer. In the first case, a flat, circular plate and a linearly concentric cone are rotated relative to each other. The cone is normally truncated so that there is no physical contact between the two. The fluid is in the space between the plate and cone. Either of the two members can be rotated or oscillated, and one measures the torque needed to keep the other member stationary. For both Newtonian... 

The cone-and-plate viscometer is one of the rotational methods of measuring the polymer viscosity. It consists of a fiat horizontal plate and a cone with an obtuse angle. The cone touches the plate at its tip and rotates at a constant speed. The melt is charged into the gap forming between the horizontal plate and the cone. The rotational velocity determines shear rate and the torque applied gives shear stress. Shear rate is constant across the gap, thus it eliminates the need for non-Newtonian behavior of the melt. In a plate-plate viscometer, the cone is replaced by a second flat plate. The Couette viscometer is comprised of two concentric cylinders where one can be rotated at a constant speed. 

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